Question

a 60 litre solution of alcohol and water contains 20 litre of alcohol. how much alcohol must be added to produce a solution of 50% alcohol?

Answer 1

Total solution = 60 L
Alcohol in solution = 20 L
Let x L alcohol must be added to produce 50% alcohol.
Then alcohol in solution at last = (x + 20) L
Total solution at last = (60 + x) L
Now,
     Alcohol at last is equal to 50% of total solution.
     x + 20 = 50(60 + x)/100
 ⇒ x + 20 = (60 + x)/2
 ⇒ x + 20 = 30 + x/2
 ⇒ x - x/2 = 30 - 20
 ⇒ (2x - x)/2 = 10
 ⇒ x/2 = 10
 ⇒ x = 10 * 2
 ⇒ x = 20

Therefore, 20L of alcohol must be added in 60L solution to get 50% alcohol in the solution.

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Answer 2

let x L of alcohol be added so total alcohol =( 20 + x )L
total solution =( 60 + x ) L
to get  50 % 
(x + 20)/(x + 60) * 100 = 50
⇒ x = 20 L